Proof: Write Decrement If Unchanged Stack At 14

Let's prove the following theorem:

if the following are true:

the line at time 14 = 5
the tab at time 14 = 1
stack at time 14 = [ ]
number of lines = 5 - 1
Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ]

then stack at time 15 = [ ]

Proof:

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Given

1	the line at time 14 = 5
2	the tab at time 14 = 1
3	stack at time 14 = [ ]
4	number of lines = 5 - 1
5	Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ]

Proof Table

#	Claim	Reason
1	value at (1 - 1) in map (Control Map at time 14) = pair ("if", False)	if Control Map at time 14 = [ entry 0: (pair ("if", False)), [ ] ], then value at (1 - 1) in map (Control Map at time 14) = pair ("if", False) (Get Decrement Key Value Control Map At 14)
2	stack at time (14 + 1) = stack at time 14	if the line at time 14 = 5 and the tab at time 14 = 1 and number of lines = 5 - 1 and value at (1 - 1) in map (Control Map at time 14) = pair ("if", False), then stack at time (14 + 1) = stack at time 14 (Decrement Tab At If End (5))
3	stack at time (14 + 1) = [ ]	if stack at time (14 + 1) = stack at time 14 and stack at time 14 = [ ], then stack at time (14 + 1) = [ ] (Transitive Property of Equality)
4	14 + 1 = 15	14 + 1 = 15 (Fixed Value Statement)
5	stack at time (14 + 1) = stack at time 15	if 14 + 1 = 15, then stack at time (14 + 1) = stack at time 15 (Substitution)
6	stack at time 15 = [ ]	if stack at time (14 + 1) = stack at time 15 and stack at time (14 + 1) = [ ], then stack at time 15 = [ ] (Transitive Property of Equality Variation 2)

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